Guernsey FC were ahead with the game just a couple of minutes old, Sam Murray putting a loose ball away.
His second came five minutes later as he slid in to turn in Charlton Gauvain’s cross from the right.
The momentum stayed with the Green Lions, and Matt Loaring scored from six yards after some great work from Ben Acey down the left for their third and his fourth in three games.
It could have been four after Ross Allen was brought down in the box to win a penalty.
South Park’s Danny Dudley was booked for that challenge and then saw red for his complaints.
But Allen hit the crossbar.
With their opponents down to 10, GFC were dominant in the second half but could not add to their tally.
They climbed one place above Ashford Town in the league to 20th spot ahead of a busy run of fixtures that include a Boxing Day trip to second placed Kingstonian and then two home games, against Hartley Wintney, who are fifth, on Saturday and Sutton Common Rovers on New Year’s Day.
All the matches kick off at 2pm.
